[Verse 1] When your binary search tree starts leaning to one side Height difference of two means balance has died Left heavy or right heavy, the structure's getting slow Time to spin those nodes and make the data flow Four cases to remember when rotation's what you need Left-left, left-right, right-right, right-left indeed Single rotation handles straight line formations Double rotation fixes the zigzag situations [Chorus] Rotate left when right side's heavy Rotate right when left's not steady Pivot point becomes the new root Balance factor stays absolute Single spin for straight lines clean Double spin for zigzag scenes Keep it balanced, keep it tight AVL rotations make it right [Verse 2] Left-left case means trouble on the left side's left Single right rotation puts balance back in effect Take the left child, make it the new root node Right subtree of new root is where old root goes But when it's left-right, that's a different game First rotate left child left, then the whole thing's tamed Two-step process, double rotation flow Zigzag pattern straightened, now your tree can grow [Chorus] Rotate left when right side's heavy Rotate right when left's not steady Pivot point becomes the new root Balance factor stays absolute Single spin for straight lines clean Double spin for zigzag scenes Keep it balanced, keep it tight AVL rotations make it right [Verse 3] Right-right heavy, single left's the cure Promote the right child, balance is assured Right-left zigzag needs the double play Rotate right child right, then left all the way After every insertion, check the balance state Negative two or positive two means don't wait Bubble up from bottom, fix what needs repair Self-balancing structure with logarithmic flair [Bridge] Height minus height equals balance factor score Negative means left heavy, positive means right has more Zero means perfect balance, that's the goal we seek Rotations keep us stable, performance at its peak [Outro] Four rotations master, keep your tree in line Search and insert guaranteed in logarithmic time AVL tree rotations, the foundation of the code Balanced data structures on the algorithmic road
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